In a △ABC if $$cos$$⁡Acos⁡Bcos⁡$$C=3$$−$$18$$ and $$sin$$⁡Asin⁡Bsin⁡$$C=3+38$$, thenThe value of $$tan$$ A $$+$$ $$tan$$ B $$+$$ $$tan$$ C is The value of $$tan$$ A $$tan$$ B $$+$$ $$tan$$ B $$tan$$ C $$+$$ $$tan$$ C $$tan$$ A isThe respective values of $$tan$$ A ,$$tan$$ B and $$tan$$ C are

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In a △ABC if $$cos$$⁡Acos⁡Bcos⁡$$C=3$$−$$18$$ and $$sin$$⁡Asin⁡Bsin⁡$$C=3+38$$, thenThe value of $$tan$$ A $$+$$ $$tan$$ B $$+$$ $$tan$$ C is The value of $$tan$$ A $$tan$$ B $$+$$ $$tan$$ B $$tan$$ C $$+$$ $$tan$$ C $$tan$$ A isThe respective values of $$tan$$ A ,$$tan$$ B and $$tan$$ C are

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∴$$cos$$⁡Acos⁡Bcos⁡$$C=3$$−$$18sin$$⁡Asin⁡Bsin⁡$$C=3+38$$∴$$tan$$⁡Atan⁡Btan⁡$$C=3+33$$−$$1$$....(1)Now$$ tanA $$+$$ $$tan$$ B $$+$$ tanC $$=$$ tanA tanB $$tanC=3+33$$−$$1$$....$$(2)Now$$ $$A+B+C=$$π∴$$cos$$⁡$$(A+B+C)=$$−$$1$$∴$$cos$$⁡Acos⁡Bcos⁡C[$$1$$−Σ$$tan$$⁡Atan⁡B]$$=$$−$$1$$∴$$3$$−$$18$$[$$1$$−Σ$$tan$$⁡Atan⁡B]$$=$$−$$1$$⇒Σ$$tan$$⁡Atan⁡$$B=5+43$$.....$$(3)From$$ $$(1), (2) and (3), we gettan A, $$tan$$ B, $$tan$$ C are roots $$ofx3$$−$$3+33$$−$$1x2+(5+43)x$$−$$(3+3)3$$−$$1=0or$$ $$x3$$−$$(2+3)3x2+(5+43)x$$−$$(2+3)3=0or$$  $$x3$$−$$(3+23)x2+(5+43)x$$−$$(3+23)=0or$$ $$(x$$−$$1)(x$$−$$3)(x$$−$$(2+3))=0$$∴    $$tan$$⁡$$A=1$$,$$tan$$⁡$$B=3$$,$$tan$$⁡$$C=2+3$$

In a △ABC if cos⁡Acos⁡Bcos⁡C=3−18 and sin⁡Asin⁡Bsin⁡C=3+38, thenThe value of tan A + tan B + tan C is The value of tan A tan B + tan B tan C + tan C tan A isThe respective values of tan A ,tan B and tan C are

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